On set-valued stochastic integrals and fuzzy stochastic equations

In this paper we extend the notion of set-valued and fuzzy stochastic integrals to semimartingale integrators. We present their main properties and finally we establish the existence of solutions of a fuzzy integral stochastic equation driven by a Brownian motion. The approach is based on the existence of solutions of an appropriately formulated martingale problem for a system of stochastic inclusions and the theorem of Negoita and Ralescu.